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The Planck length, denoted ℓP, is a unit of length defined as:ℓP=ℏ��3
It is equal to 1.616255(18)×10−35 m,[7] where the two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value, or about 10−20 times the diameter of a proton
It can be motivated in various ways, such as considering a particle whose reduced Compton wavelength is comparable to its Schwarzschild radius,[29][30][31] though whether those concepts are in fact simultaneously applicable is open to debate.[32] (The same heuristic argument simultaneously motivates the Planck mass.[30])
The Planck length is a distance scale of interest in speculations about quantum gravity. The Bekenstein–Hawking entropy of a black hole is one-fourth the area of its event horizon in units of Planck length squared.[11]: 370 Since the 1950s, it has been conjectured that quantum fluctuations of the spacetime metric might make the familiar notion of distance inapplicable below the Planck length.[33][34][35] This is sometimes expressed by saying that “spacetime becomes a foam at the Planck scale“.[36] It is possible that the Planck length is the shortest physically measurable distance, since any attempt to investigate the possible existence of shorter distances, by performing higher-energy collisions, would result in black hole production. Higher-energy collisions, rather than splitting matter into finer pieces, would simply produce bigger black holes.[37]
The strings of string theory are modeled to be on the order of the Planck length.[38][39] In theories with large extra dimensions, the Planck length calculated from the observed value of � can be smaller than the true, fundamental Planck length.[11]: 61 [40]
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